Find a quadratic equation whose product of roots `x_1a n dx_2` is equal to 4 an satisfying the relation `(x_1)/(x_1-1)+(x_2)/(x_2-1) =2.`

Evaluate: int(x+1)/((x-1)^(2)(x+2))dx .

Evaluate int_(-1)^(1)(x^2)/(x^2+1)dx .

Evaluate int(2x-1)/((x-1)(x+2))dx .

Find the roots of the equation (1)/(x)-(1)/(x-2)=3, x ne 0,2

Evaluate int (x-1)/(x^2-2x+1)dx

Find the number of positive integral solutions satisfying the equation (x_1+x_2+x_3)(y_1+y_2)=77.

Let S be the set of all non-zero real numbers such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1a n dx_2 satisfying the inequality |x_1-x_2|<1. Which of the following intervals is (are) a subset (s) of S ? (1/2,1/(sqrt(5))) b. (1/(sqrt(5)),0) c. (0,1/(sqrt(5))) d. (1/(sqrt(5)),1/2)

Evaluate int (x+1)/(x^2+2x+1) dx

Let S be the set of all non-zero numbers alpha such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1, and x_2 satisfying the inequality |x_1-x_2|lt1 which of the following intervals is(are) a subset of S?

The value of x that satisfies the relation x=1 -x+x^2-x^3+x^4-x^5+….oo is